1 MINISTRY OF EDUCATION AND TRAINING MINISTRY OF NATIONAL DEFENCE ACADEMY OF MILITARY SCIENCE AND TECHNOLOGY VU DINH MINH RESEARCH ON DEVELOPMENT OF SEMI-SUPERVISED CLUSTERING ALGORITHMS USING FUZZY MIN-MAX NEURAL NETWORK AND THEIR APPLICATIONS Specialization: Mathematical Foundation for Informatics Code: 46 01 10 SUMMARY OF PhD THESIS IN MATHEMATICAL Hanoi, 2019 This thesis has been completed at: ACADEMY OF MILITARY SCIENCE AND TECHNOLOGY Scientific supervisors: Assoc Prof Dr Le Ba Dung Dr Nguyen Doan Cuong Reviewer 1: Assoc Prof Dr Bui Thu Lam Military Technical Academy Reviewer 2: Assoc Prof Phung Trung Nghia Thai Nguyen University Reviewer 3: Dr Nguyen Do Van Academy of Military Science and Technology The thesis was defended at the Doctoral Evaluating Council at Academy level held at Academy of Military Science and Technology at date ……., 2019 The thesis can be found at: - The library of Academy of Military Science and Technology - Vietnam National Library INTRODUCTION The necessary of the thesis Fuzzy semi-supervised clustering is an extension of fuzzy clustering using prior knowledge that increases quality of clusters Pre-informed information, also known as additional information, is intended to guide, monitor and control the clustering process Fuzzy min-max neural network (FMNN) model proposed by Patrick K Simpson is based on advantages of combining fuzzy logic, artificial neural network, fuzzy min-max theory to solve classing and clustering problem FMNN is an incremental learning model based on fuzzy metafiles for ability to process large data sets Liver disease diagnosis based on data from liver enzyme test results can be formulated as a pattern recognition problem Use of FMNN is considered an effective approach One of the reasons that FMNN is used in disease diagnostic support is the ability to generate if…then decision rule that is very simple Each FMNN's hyperbox transforms into a rule described by quantifying and max values of the data attributes However, the FMNN itself still has many shortcomings leading to the difficulties and limited practical application Main researches on FMNN focus on major directions such as improving the network structure, optimizing parameters, subscribing, reducing the number of hyperbox in the network, improving the learning method or incorporating other method to improve the quality Based on the research on FMNN's development process, to improve the efficiency of FMNN, the thesis topic focuses on proposing and improving methodology by semi-supervised learning method In the new methods presented in the thesis, additional information is defined as the label assigned to a piece of data to guide and monitor the clustering process This is a new approach that earlier methods have not mentioned 2 Objectives of the research 1) Develop advanced fuzzy semi-supervised clustering algorithm based on label spreading Additional information is a small percentage of the samples labeled 2) Propose a novel model of combined semi-supervised clustering, this model automatically defines additional information In our research, a part of sample of the fuzzy semi-supervised clustering algorithm is labeled 3) Develop a fuzzy clustering algorithm considering to the distribution of data 4) Apply fuzzy min-max neural network to the dump of fuzzy if then decision rule in design of the liver disease diagnostic support system from data is data of the results of the liver enzyme test Object and scope of the research The thesis focuses on the following issues: - An overview of fuzzy min-max neural network and variations of fuzzy min-max neural network - Analysis of limitations and solutions used by researchers to overcome these limitations - Application of fuzzy min-max neural network with dump of fuzzy if then decision rule in disease diagnosis Research methods The thesis uses theoretical research method, in particular, the thesis has studied the FMNN model for classing and clustering data Since then, the thesis focuses on the proposed semi- supervised clustering algorithm The thesis also uses simulated empirical method in combination with analysis, statistics and evaluation of empirical data Contribution of the thesis - Develop the advanced SS-FMM algorithm for fuzzy semisupervised clustering based on label spreading progress - Propose a novel model of semi-supervised clustering combined with FMNN and SS-FMM This model automatically defined additional information for semi-supervised clustering algorithms - Develop a fuzzy clustering algorithm considering to the distribution of data Structure of the thesis Apart from the introduction and conclusion, the main contents of the thesis consists of three chapters: - Chapter presents an overview of the thesis, including the basic concepts of FMNN and FMNN extensions From general characteristics of extensions, limitations, it shall provide the direction of the next research Throughout this chapter, the thesis gives an overview of the research problem, concepts and basic algorithms used in the research - Chapter presents suggestions for improving learning method in the FMNN using the semi-supervised algorithm model for data clustering The additional information is labeled a part of the sample in the training data set Then labels from this part of data are spreading to unlabeled data samples Fuzzy semi-supervised clustering combining with FMNN model automatically defines additional information This is also used as the input of the fuzzy semi-supervised algorithm Data clustering model in fuzzy min-max neural network takes into account distribution of data as well - Chapter presents the application of proposed model with the generation of fuzzy decision rules formed if then in support system of liver disease diagnostic on a real dataset Chapter 1: Overview of fuzzy min-max neural network 1.1 Fundamental knowledge of fuzzy min-max neural network * Hyperbox membership function The degree determination of membership function bj(A,Bj) measures the degree of belonging of sample A corresponding to hyperbox Bj It is defined by Eq (1.2) or Ed (1.3) below   b j A, B j     n   max 0,1  max 0,  1,  w ji 2n i 1      + max 0,1  max 0,  1, v ji    b j A, B j      (1.2)    n    f  w ji ,   f v ji  ,    n i 1  (1.3) * Fuzzy min-max neural network structure FMNN uses a straight-forward neural network structure, two-layer structure (Fig 1.4) with unsupervised learning and three-layer structure (Fig 1.5) with supervised learning Fig 1.4 Two-layer neural network model Fig 1.5 Three-layer neural network model * Overlapping between hyperboxes The FMNN algorithm is aimed at creating and modifying hyperboxes in n-dimensional spaces If the expansion creates overlap between the hyperboxes, the contraction process is performed to eliminate overlap The overlap happens between Bj and Bk if one of the four following cases occurs: - Case 1: max of Bj overlapped with of Bk - Case 2: of Bj overlapped with max of Bk - Case 3: Bk contained within Bj - Case 4: Bj contained within Bk If Bj and Bk are overlapped, the contraction process of hyperboxes is performed in the corresponding direction to eliminate overlap: - Case If v ji  vki  w ji  wki then: new vkinew   vkiold  wold   vkiold  wold ji  / wki ji  / - Case If vki  v ji  wki  w ji then: old new old v new   vold   vold ji ji  wki  / wki ji  wki  / - Case If v ji  vki  wki  w ji , considerring following cases: + If (wki  v ji  wji  vki ) , then: vnew  wkiold ji + If (wki  v ji  wji  vki ) , then: wnew  vkiold ji - Case If vki  v ji  w ji  wki , considerring following cases: + If (wki  v ji  wji  vki ) , then: wkinew  vold ji new old + If (wki  v ji  wji  vki ) , then: vki  w ji * The learning algorithm in fuzzy min-max neural netwwork Algorithm in fuzzy min-max neural network only include creation and modification of hyperboxes in the sample space The learning algorithm in FMNN consists of steps: creation and expansion of hyperboxes, overlapping test, hyperbox contraction Each step is repeated for all samples in the dataset 1.2 Some researches to improve quality of FMNN * Adjust size limit of hyperbox In order to overcome the phenomenon of exceeding size limit of hyperbox for network training due to the averaging method, D Ma proposed an alternative solution of size limit function to be compared in all dimensions calculated according to formula (1.24) using the formula (1.29)  A, B   j  A , B    h j       max  w , a   v , a  n  max w ji ,  v ji , , n i 1 i 1, ,n ji hi ji hi (1.24) (1.29) * Modify FMNN structure to manage overlapping areas The FMCN (Fuzzy Min-max neural network classifier with Compensatory Neurons) and DCFMN (Data-Core-Based Fuzzy Min– Max Neural Network) models overcome the problems caused by contraction of the hyperboxes that created the additional hyperboxes Rather than adjusting contraction of the hyperboxes, the FMCN and DCFMN handle overlapping areas by using hyperboxes to manage separate overlapping area * Improve learning method in FMNN The semi-supervised model of GFMM (General Fuzzy Min-Max) and RFMN (Reflex Fuzzy Min-max Neural network) uses additional information as the labels accompanying with some input patterns GFMM and RFMN used prior knowledge to monitor and guide clustering 1.5 Conclusion of Chapter Chapter presented the overview research on FMNN and development trend of FMNN, synthesized and compared the case researches on structural improvement of FMNN algorithm The following chapters will present proposals on some issues that remain in development of FMNN and application of FMNN to support disease diagnosis Chapter 2: The development of semi-supervised clustering algorithm using fuzzy min-max neural network This chapter presents three algorithms to improve learning method and the experimental results used to evaluate proposed algorithms The novel models include: - An improvement of SS-FMM semi-supervised learning method, results announced in [3] - A novel model of semi-supervised clustering combined with FMNN and SS-FMM, results announced in [5] - A fuzzy clustering algorithm considering to the distribution of data In addition, the algorithm uses a set of additional rules in the training process Results announced in [2, 4] 2.1 SS-FMM semi-supervised fuzzy clustering algorithm The GFMM model and the modified model (RFMN) have the advantage of using more prior information to monitor the clustering process, thereby improving the clustering quality However, both GFMM and RFMN are capable of producing hyperboxes with their own attributes that are not labeled Because when GFMM and RFMN create new hyperboxes for the first sample with out label, the new hyperbox is not labeled This hyperbox will wait for labeled samples to edit the label of the hyperbox by the label of the sample However, there may still be unlabeled hyperboxes that are not edited due to the absence of labeled samples Figure 2.1 is an illustrative example of the case of GFMM and RFMN producing unlabeled hyperboxes Hyperbox Siêu hộp U Hyperbox Siêu hộp V V Fig 2.1 Failed hyperboxes of GFMM and RFMN Where: V is a hyperbox created from labeled samples or be adjusted label by labeled samples, U is a hyperbox created from unlabeled samples or without label adjustment The SS-FMM algorithm proposes the method to overcome this disadvantage of GFMM and RFMN SS-FMM prevents the algorithm from making unlabeled hyperboxes using the β-limit threshold The initial threshold is defined by user, but the algorithm has the ability to manually redefine the threshold for fit during training process The framework diagram is described in Figure 2.2 When creating a new hyperbox from the unlabeled pattern, SS-FMM only creates a new hyperbox if it satisfies β criteria defined in (2.2)   max  E A , B : j  1, , q    ,   h j   (2.2) The SS-FMM operates under the label spreading scheme to label hyperboxes made by unlabeled samples Algorithms generate hyperboxes from labeled data samples and spread the labels from labeled hyperboxes to the hyperboxes created by unlabeled samples SS-FMM incorporates all the hyperboxes with the same label that form a full cluster Begin Input: D,  ,  Snew = |D|; Sold = 0; m = |D|; h = Input pattern {Ah ,dh}D Does Ah belong BjB? y y n Is BjB that is able to conver Ah? y Expand of Bj n n dh = 0? d h  Blj n dh ≠ 0? y l Create Hnew, H new  dh , B  B  Hnew n D  D \  Ah  dh = ?  y d h  Blj  n max E A , B  j  1, , q   h j S old S old 1 y Is there overlapping? n y Hyperbox contraction l Create Hnew, H new  Blj B  B  Hnew D  D \ Ah  k=k+1 y n h < m? n Snew = Sold ? n y   . D  ? y Calculate C according to (1.7) Output: B, C End Fig 2.2 General diagram of SS-FMM algorithm * Complexity evaluation of the SS-FMM algorithm The SS-FMM algorithm has time complexity that is O(M(M(M-1)/2+NK) Where M is the total number of samples in the training data set, N is the number of attributes of the data sample, K is the total number of hyperboxes generated in the SS-FMM network 11 centroids of the corresponding hyper-boxes Centroid value is calculated until the sample is far away from the hyperbox and its membership is less than 0.6, when the membership function value does not decrease Apart from the and max points, each hyperbox has the center of the hyperbox defined as in (2.8)   c ji  v ji  w ji / (2.8) The Euclidean distance between the input pattern Ah and the center of hyperbox j, E A , B  is given by (2.9): h j E A , B    h j n  n i 1 c ji  ahi  (2.9) For each sample Ah satisfies the size limit condition (1.24) where the membership function value is bj < 0.6, its distance is calculated and compared with others Samples will belong to the closest hyperboxes * Complexity of the CFMNN algorithm CFMNN algorithm has a time complexity of O(MKN) Where M is the total number of samples in the training data set, N is the number of attributes of the data sample, K is the total number of hyperboxes generated in CFMNN 2.4 Experiment and evaluation * Experimental method To evaluate the performance of these proposed algorithms, the experiments were performed on the Benchmark data set The objective of experiment is to evaluate the ability to improve performance, quantity, and distribution of the hyperboxes when changing the value of parameter max in the SS-FMM, CFMNN, SCFMN algorithms This also evaluates the mitigation capability of hyperboxes as well Accuracy and CCC (Cophenetic Correlation Coefficient) measurements are used to evaluate the performance of algorithms and compare them to other ones Accuracy is calculated by (2.12), CCC is calculated by (2.13) 12 Details of the experimental results are presented in Table 2.2 to Table 2.14, from Figure 2.9 to Figure 2.20 * Experimental results (a) Spiral (b) Aggregation (c) Jain (d) Flame (e) Pathbased (b) R15 Fig 2.9 Graphical distribution of hyperboxes on data sets 13 (a) (b) (c) (d) Fig 2.10 Accuracy obtained when changing the ratio of labeled sample of SS-FMM 14 (a) Data set R15 (b) Jain data set (c) Iris data set (d) Flame data set Fig 2.11 Accuracy obtained when changing max of SS-FMM and SCFMN 15 (a) Jain dataset (b) Flame dataset (c) Iris dataset (d) R15 dataset Hình 2.17 NoH obtained when changing max of SS-FMM and SCFMN The experimental results show that: 16 - Accuracy decreases when ratio of the labeled sample decreases but it is not as much as the decreasing ratio of the labeled sample in training set - Accuracy decreases when the max size of max increases When max is too small, the Accuracy measurement decreases max affects to the performance of the algorithm - The total number of hyperboxes decreases when max increases * Comparisons of proposed algorithm results with some other algorithms Table 2.7 compares the GFMM, RFMN and SS-FMM Accuracy measurements on the Iris data set Table 2.7 Values of Accuracy with the changing of ratio of sample labeled Accuracy (%) Ratio of sample labeled GFMM RFMN SS-FMM 2% 36 52 94 10% 49 83 96 50% 84 92 97 Table 2.8 compares the GFMM, RFMN and SS-FMM Accuracy measurements on a set of experimental data sets Sample ratio in label in training training is 10% Table 2.8 Values of Accuracy obtained by using SS-FMM, GFMM and RFMN on different data sets Data set Aggregation Flame Jain Sprial Pathbased R15 Iris ThyroidNew Wine Accuracy (%) GFMM RFMN SS-FMM 48.25 79.56 98.86 49.74 84.47 98.75 56.32 55.19 52.47 48.28 49.36 51.83 52.54 85.35 82.61 82.52 84.78 83.92 80.12 80.73 100 100 98.72 99.50 96.00 91.69 93.33 17 Table 2.9 Comparison of Accuracy obtained by using SCFMN, CFMNN, FMNN and MFMM Accuracy (%) Data set FMNN MFMM CFMNN SCFMN Flame 85.13 91.78 91.25 99.17 Jain 86.07 91.18 91.20 100 R15 87.24 93.54 93.76 99.50 Iris 86.97 93.01 92.77 95.98 Wine 85.58 93.12 92.83 94.35 PID 68.35 70.08 70.49 74.58 Table 2.10 Compare of CCC obtained by using SCFMN, CFMNN, MFMN and MFMM CCC Data set Glass Iris Wine MFMM MFMN CFMNN SCFMN 0.94 0.94 0.93 0.94 - 0.97 0.97 0.98 0.83 - 0.84 0.89 Table 2.11 Compare Time obtained by using SCFMN, CFMNN, FMNN and MFMM Dataset Time (s) FMNN MFMM CFMNN SCFMN Flame 0.483 0.532 0.487 0.876 Jain 0.635 0.724 0.648 0.923 R15 0.701 0.798 0.712 0.967 Iris 0.215 0.231 0.221 0.623 Wine 0.274 0.283 0.276 0.692 525.132 732.945 543.675 913.657 PID 18 Hình 2.19 Values of Accuracy comparison chart of SCFMN, CFMNN with FMNN, MFMM Figure 2.20 NoH comparison chart of SCFMN with some other methods 2.5 Conclusion of Chapter Chapter presents the improvements of FMNN algorithm including: - Propose improvements of semi-supervised learning with labeled a part of the data in training set and label spreading methods (SS-FMM) Learning algorithm in SS-FMM uses the information contained in both of labeled and unlabeled data for training SS-FMM performs well even with low ratio of labeled samples This proposal was published in [3] - Propose a novel semi-supervised clustering model combined (SCFMN) SCFMN uses semi-supervised learning method with additional information defined automatically SCFMN uses structure of hyperbox with large size at the center of the cluster to minimize the number of hyperboxes and small hyperboxes at the boundary among the clusters to increase clustering performance This proposal was published in [5] 19 - Propose an improved algorithm CFMNN considering to the distribution of data In the forecasting and adjusting stages, the hyperbox is not completely dependent on its membership degree, especially when the model is far away from the hyperbox In addition, the CFMNN uses a new set of 10 rules to adjust hyperboxes during training This proposal has been published in [2, 4] Chapter 3: Application of Fuzzy min-max neural network in supporting liver disease diagnosis 3.1 Liver disease diagnosis methods * Diagnosed using APRI APRI is calculated by the formula (3.1): APRI = AST / ULN  100 PLT (3.1) * Diagnosed using FIB-4 FIB-4 is calculated by the formula (3.2): FIB-4 = Age  AST PLT  ALT (3.2) 3.2 Liver disease diagnosis support using fuzzy min-max neural network * Problem modeling CDS (Cirrhosis Diagnosis System) is a diagnostic model for liver disease based on a combination of fuzzy min-max theory, artificial neural networks and fuzzy inference method to build a decision support system via data of liver enzyme test The model of CDS in liver disease diagnostic support system is shown in Figure 3.1 * Model analysis - CDS creates an combined approach between data clustering algorithm and decision-making methods for the liver disease diagnosis - CDS offers a view to combine clustering algorithm using FMNN with the decision-making system This has great significance for liver disease diagnosis problem in particular and the fields of Medical Informatics in general 20 Begin Liver enzyme test Extract and select features Expansion of hyperbox Data Hyperbox Overlap Test Hyperbox Contraction Fuzzy min-max neural network training Pruning Hyperboxes Generating the Rules Disease summary table from the test results Diagnostic End Fig 3.1 Liver disease diagnostic support system by CDS * Pruning hyperbox using the HCF index Each hyperbox is associated with an HCF (Hyperbox Confidence Factor) to measure usage level Hyperboxes with a HCF index lower than the threshold will be pruned * Decision rule extracting Each hyperbox generates a fuzzy decision rule The and max values are quantified as Q levels that equivalent to the number of fuzzy partitions in the quantitative rule Each input pattern is assigned to quantum dots by using (3.8): Aq  (q  1) / (Q  1) Fuzzy rules formed if…then are defined by (3.9): Rule R j : If x p1 is Aq and  x pn is Aq Then x p is C j (3.8) (3.9) 21 3.3 Experiment and evaluation * Experimental data sets Information on liver disease data is shown in Table 3.3 This information is extracted from the medical records related to the test results and disease diagnosis from doctors * Objectives of experiments - To evaluate the ability of improving the performance - To evaluate the number of hyperboxes before and after prunning process - To evaluate the decision rules, computation time * Measurements and evaluation criteria Measurements include Accuracy, AccSe, AccSp, NPV, PPV, Jaccard, Rand, FM, NoH * Experimental results Details of the experimental results are presented in Tables 3.4 to Table 3.15, from Figure 3.2 to Figure 3.10 (a) SS-FMM (b) SCFMN Fig 3.5 Accuracy of SCFMN, SS-FMM when changing max on Liverdisease dataset 22 Fig 3.6 NoH of SCFMN and SS-FMM when changing max on real dataset Table 3.9 Fuzzy rules on Cirrhosis dataset generated by SCFMN IF Rule Then CF A1 A2 A3 1 2-3 0.300 1-3 2-3 0.114 1-2 3-4 0.075 3-4 1-2 1 0.039 1-3 1-4 1-2 0.834 1 1-4 0.43 Table 3.13 An example of a diagnostic results using SCFMN on real dataset If Then (C) A1 81 A2 A3 A4 97.1 104.1 A5 A6 3.1 154.4 A7 36.7 A8 27.3 A9 10.1 A10 37 53 94.1 100.9 3.1 266.4 25.2 37.6 10.7 28 53 87.9 94.3 3.1 249.0 23.5 35.1 10.0 28 81 86.1 92.3 3.1 136.9 32.5 24.2 9.0 37 24 592.3 200.6 3.0 195.6 38.3 359.5 139.3 39 37 568.6 208.7 2.7 82.6 27.5 65.3 15.3 23 46 60.4 57.0 1.1 87.8 37.4 19.0 3.5 18 57 60.5 45.4 1.3 196.2 39.2 12.1 3.5 29 57 60.5 45.4 1.3 196.4 39.2 12.1 3.5 29 3.4 Conclusion of Chapter In chapter 3, the applications of proposed models in the design of support system for diagnosing liver disease from data which includes the information of liver enzyme tests 23 The implement of proposed models on the live disease data set Obtained results show that proposed models get better results comparing with giving good results with predicted values Especially the ability to extract the fuzzy if then decision rule with quantitative values are the min-max points of the fuzzy hyperbox The results were evaluated through measurements, and at the same time, through these experimental results, once again test the correctness of the propositions when constructed using theoretical models CONCLUSION From the research contents, the thesis has achieved the following results: * Main results: - Propose algorithm improvements with semi-supervised learning using additional information is labeled with part of the data in the training set and label spreading methods (SS-FMM) It gradually forms and corrects the hyperboxes (clusters) during training Labeled samples are pre-populated to form hyperboxes, and then spread the labels to unlabeled samples to form hyperboxes from unlabeled training samples Learning in SS-FMM uses the information contained in the labeled data and also unlabeled data for training SS-FMM performs well even with low labeled sample rates This proposal was published in [3] - Propose fuzzy semi-supervised clustering model combined between SS-FMM and FMNN The proposed model uses semi-supervised learning method with additional information provided by automatically defined algorithms The algorithm uses structure of hyperbox with large size at the center of the cluster to minimize the number of hyperboxes and small hyperboxes at the boundary among the clusters to increase clustering performance This proposal was published in [5] - Propose algorithm for improving CFMNN considering to the distribution of data During the forecasting and adjustment phase, the hyperbox is not completely dependent on its dependency, especially when the model is far away from the hyperbox In addition, the CFMNN 24 uses a new set of 10 rules to adjust hyperboxes during training This proposal has been published in [2, 4] - Propose fuzzy min-max neural network application model with the fuzzy if then decision rule in design of the liver disease diagnostic support system is the data of the results of the liver enzyme test of patient The fuzzy if then decision rules are derived from the set of hyperboxes after removal of low-consumption hyperboxes Experiment of proposed model gave good results on the Benchmark dataset from the UCI, CS database and data is is the data of the results of the liver enzyme test of patient Especially the ability to extract the fuzzy if then rule is very simple with quantitative values are the min-max points of the fuzzy hyperbox The results were evaluated through measurements, and at the same time, through these experimental results, once again test the correctness of the propositions when constructed using theoretical models * New contributions: 1) Develop the SS-FMM semi-supervised clustering algorithm based on label spreading 2) Propose a novel model of semi-supervised clustering combined with FMNN and SS-FMM This model automatically defined additional information for semi-supervised clustering algorithms 3) Develop a fuzzy clustering algorithm considering to the distribution of data * Recommendations and next research direction: Besides the results obtained, the thesis opens a number of research directions to improve the quality and applicability of fuzzy min-max neural network: - Improve the method of pruning hyperbox in fuzzy min-max neural network to reduce the number of rules - Continue research on the diagnosis of liver disease based on clinical symptoms and imaging diagnosis LIST OF SCIENTIFIC PUBLICATIONS Vũ Đình Minh, Nguyễn T.Việt Hương, Lê Bá Dũng (2015) Mạng nơron phân cụm mờ max dựa tâm khoảng cách Euclidean Tạp chí Khoa học Cơng nghệ Đại học Thái Nguyên, 14(144), Tr.11-16 Vu, D M., Nguyen, T V H., Chu, T T G & Le, B D (2016), An Increased Fuzzy Min-Max Neural Network for Data Clustering Journal of Science & Technology Technical Universities,113, Tr.125-129 Vu, D M., Nguyen, V H., & Le, B D (2016), Semi-supervised Clustering in Fuzzy Min-Max Neural Network In International Conference on Advances in Information and Communication Technology (pp 541-550) Springer international Publishing Vũ Đình Minh, Nguyễn Dỗn Cường, Nguyễn Thị Lan Hương (2017), Mạng nơron phân cụm min-max mờ dựa tâm cụm liệu Tạp chí Nghiên cứu Khoa học Công nghệ Quân sự, Tr.20-32 Tran, T N., Vu, D M., Tran, M T., & Le, B D (2018), The Combination of Fuzzy Min–Max Neural Network and Semisupervised Learning in Solving Liver Disease Diagnosis Support Problem Arabian Journal for Science and Engineering, -12 DOI: 10.1007/s13369-018-3351 -7 Vũ Đình Minh, Nguyễn Dỗn Cường (2018) Học bán giám sát mạng nơron max mờ cho phân cụm liệu với rút trích luật định Tạp chí Nghiên cứu Khoa học Cơng nghệ Qn sự, Tr.17-26 Vu, D M., Tran, T N., Tran, M T., Le, B D., & Nguyen D C (2018) Fuzzy Min Max Neural Network and Genetic Algorithm in Diagnosing Liver Related Diseases Proceedings of International Conference on Frontiers of Intelligent Computing: Theory and Applications (FICTA - 2018), In Springer Link ... (2017), Mạng nơron phân cụm min- max mờ dựa tâm cụm liệu Tạp chí Nghiên cứu Khoa học Công nghệ Quân sự, Tr.20-32 Tran, T N., Vu, D M., Tran, M T., & Le, B D (2018), The Combination of Fuzzy Min Max. .. 10.1007/s13369-018-3351 -7 Vũ Đình Minh, Nguyễn Dỗn Cường (2018) Học bán giám sát mạng nơron max mờ cho phân cụm liệu với rút trích luật định Tạp chí Nghiên cứu Khoa học Công nghệ Quân sự, Tr.17-26... and imaging diagnosis LIST OF SCIENTIFIC PUBLICATIONS Vũ Đình Minh, Nguyễn T.Việt Hương, Lê Bá Dũng (2015) Mạng nơron phân cụm mờ max dựa tâm khoảng cách Euclidean Tạp chí Khoa học Cơng nghệ Đại